Code Golf: Shortest code to find a weighted median?

Question

My try at code golfing.

The problem of finding the minimum value of ∑W_i*|X-X_i| reduces to finding the weighted median of a list of x[i] with weights <

Answer 1

J

Go ahead and type this directly into the interpreter. The prompt is three spaces, so the indented lines are user input.

   m=:-:@+/@(((2*+/\)I.+/)"1@(,:(\:i.@#))@[{"0 1(,:(\:i.@#))@])

The test data I used in my other answer:

   1 1 1 1 m 1 2 3 4
2.5
   1 1 2 1 m 1 2 3 4
3
   1 2 2 5 m 1 2 3 4
3.5
   1 2 2 6 m 1 2 3 4
4

The test data added to the question:

   (>:,:[)i.10
1 2 3 4 5 6 7 8 9 10
0 1 2 3 4 5 6 7 8  9
   (>:m[)i.10
6
   (([+<&6),:>:)i.9
1 2 3 4 5 6 6 7 8
1 2 3 4 5 6 7 8 9
   (([+<&6)m>:)i.9
6.5

---

   i =: (2 * +/\) I. +/

First index such that total sum is greater than or equal to double the accumulated sum.

   j =: ,: (\: i.@#)

List and its reverse.

   k =: i"1 @ j @ [

First indices such that -see above- of the left argument and its reverse.

   l =: k {"(0 1) j @ ]

Those indices extracted from the right argument and its reverse, respectively.

   m =: -: @ +/ @ l

Half the sum of the resulting list.